According to prior art, it is common to use a so-called conic fit, i.e. a Morse conic fit, for fixing a tool, whereby the tool frame and the tool holder are joined to each other by a fixing movement in their axial direction, the release being effected in a corresponding manner in the axial direction. In particular, the conic fit has the disadvantage that the connecting surfaces very easily tend to be clamped too much against each other, particularly under effect of axial forces. For this reason, many systems presently in use comprise special release mechanisms for releasing clamped conic surfaces in connection with the exchange of a tool. As a natural result, the costs of fixing mechanisms required by tool settings are increased, also, the mechanisms are relatively complex and therefore subject to disturbances during the actual machining operation and particularly during the exchange of a tool.